NEW DELHI—India's voters chose a Hindu-nationalist, pro-business politician to be their next prime minister, tossing out the party that has led the country for most of the past 67 years.

Riding a wave of voter discontent with the incumbent Congress party and a sharply slowing economy, the Bharatiya Janata Party, led by Narendra Modi, was on track Saturday to win 282 of the 545 seats in the lower house of Parliament, according to the...